Function Notation and Linear Functions

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics, typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line?

Back

The slope of a line is found by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line, often expressed as m = (y2 - y1) / (x2 - x1).

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

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What is the y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is represented by the value of b in the linear function equation f(x) = mx + b.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if each input (x-value) is associated with exactly one output (y-value). If any input is linked to multiple outputs, it is not a function.

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What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is paired with exactly one output.

Front

What is the formula for finding the slope between two points?

Back

The formula for finding the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).